For those that don't believe some of the numbers, here is a quick page that will do coin flips for you. On the right is the page with a button that says "Flip coins". You can change how many flips it does at the top (do a million, something not practical by hand, and it will return in a fraction of a second on my computer at least). On the right, for those that know javascript, is the code that does it and shows it is just doing two fair flips of a coin.
But this isn't about the odds of a single child, but the odds of different families. The odds of a family with two children having two boys versus one boy versus no boys is not 25%:75%:25%. The odds of a family with three children having three, two, one, or zero boys is 12.5%:37.5%:37.5%:12.5%, and for four children, the same idea works out to 6.25%:25%:37.5%:25%:6.25%. It is a binomial distribution, assuming that the chances male vs. female of each child are exactly 50% (there is a lot of cool stuff behind the binomial expansion, e.g. how it reflects Pascal's triangle).
The question isn't asking what the chances of a particular child is boy or female, which would be 50%, but what are the chances a family with two children, would be both boys, or have one boy, knowing it isn't two girls.
As I said in my comment, it doesn't matter if you take order into consideration. In which case, yes, HT and TH are the same thing, but you no longer have equal chances of getting each of the three possibilities: TT, HT, HH. The chances of each are now 25%, 50%, and 25%, something that can be checked by flipping actual coins a pair at a time and not caring about order (an example is mentioned in a new comment of mine above). You still remove the TT example and end up with a 50:25 ratio, which goes back to HH happening a third of the time.
This is not just something that is a matter of trivia, but has real world impact. For example, this is how the probabilities work for any textbook simple genotype case. Suppose you had a recessive and dominant gene, such that there is no impact of being a mixed genotype, but a double recessive dies before birth. Order obviously doesn't matter here, only that you either have two different genes, or you have two of the same genes of one or the other. For two parents of mixed genotype, offspring get the genes randomly, so it is just like coin flips, and you will get 25% DD, 50% Dr, and 25% rr. All of the rr will die before birth, resulting in a third of the offspring being DD, and two-thirds being Dr.
Just because there are two choices doesn't mean there is a 50-50 chance. I might find 100 dollar bill today on the street, or I might not, that doesn't mean there is a 50% chance I will find a $100 bill today.
You can just look at the number of families that have kids, and see that half of them will have a mix, while a quarter have two girls, and a quarter will have two boys. Or just start doing this with coins. I even sat down with an online coin flipper, and did 100 quick flips, getting 22 MM (or HH), 54 MF (HT) and 24 FF (TT). Excluding the FF case leaves behind two groups without a 50-50 ratio, even if there are only two possibilities.
And if I remember correctly that you were the one with a biology background, think of genotypes (which I mention in another comment below).
"Wait a minute, I’ve flipped enough coins in statistics class to know that the real answer is still 50%"
No, the answer is one third, and you can check it by doing an experiment with coins (or an Excel spread sheet, or simple program). The key point is they are not giving info about one child and asking for the chance of a specific child being male or female, but saying "one" and "the other" places constraints only on the whole system. If you flip two coins, there are four equal possibilities: TT, TH, HT, HH. Even if not keeping track of order, it is TT, HT, HH with a 25%:50%:25% split. The information given allows you to only eliminate one of those (say TT), and not say which coin is heads, and either way end up with a 1:3 ratio.
You can literally test this with coins. Flip a pair of coins. If the pair is TT, don't count it and reflip. Otherwise record how many times you get HH and how many times you get one of each. With about 25 flips, you should have less than a 5% chance of getting 50% or higher. 100 flips would give you less than a thousand chance of getting 50% or more HH, and about 5% chance of getting more than 40% HH, at which point it would be rather tedious but separated from 50%.
This question comes up a lot in three contexts: lessons about the subtle meanings of words in word problems, basic level combinators/probability, or random "paradox" lists. But even like the Monty Hall probability question, people will argue until against the results of even basic experiments until the day they die.
Pretty much everything in the Gilbert Atomic Energy lab kit you can still get from educational suppliers today, is not something particularly dangerous, and can be an entertaining component to actually teaching modern physics.
From what I've seen before, it basically had four radiation detectors: Geiger-Muller tube counter (which unfortunately is and was kind of expensive, leading to cheaper kits with everything else), an electroscope, which is something you can build from household items, a phosphor based detector, and a cloud chamber. A cloud chamber lets you see paths of ionizing radiation and building one was one of the more fond memories I had from middle school. The kit also had a selection of small radioactive sources , something else still available from educational supplies (price has gone up a lot in the couple decades since I last bought some). These are not particularly dangerous as long as they are kept outside of the body, like a lot of things in our day-to-day life.
And for that matter, elemental and many other forms of mercury have virtually no evidence linking it to causing cancer in humans, with some evidence in animals for methymercury. It is still a very dangerous substance without care and not something I would give to a kid, but it is not dangerous because it causes cancer.
Copper alloys including brass will kill a lot of microscopic stuff on contact, and brass should be used where possible in such settings, but it is not the final line. It can take minutes to hours for brass to sanitize itself, so for things like some door handles that are used more frequent than that, it is only a partial solution. For less frequently used things or things that will sit for a little while, there have been studies to show it is as effective as the cleaning applied to a patient's room after they have checked out.
The circumhorizon arc isn't that rare, and is something you can see several times a year in the US (or anywhere of comparable latitude and cirrus clouds) if you know what to look for in the summer. The name 'fire rainbow' also seems to upset atmospheric scientists, because it is neither from fire or a rainbow, and the term is not historic, but was created by the news a couple years ago.
From the UK law restricting some hand weapons lists it as another name for a throwing star:
1 (h) the weapon sometimes known as a “shuriken”, “shaken” or “death star”, being a hard non-flexible plate having three or more sharp radiating points and designed to be thrown;
I assumed you were implying they were biologists. I was curious about what fields within biology they worked on. For example, I knew of some physicists with crazy physics ideas, but one example was someone who had a background and career in optics, but later went on to have way-out ideas about gravity, or another case of someone (one I didn't meet personally) who's main work was in magnetic resonance imaging, but went off the deep end about astronomy.
Just curious, were they older profs, and how closely were those statements to their main fields of research? I've seen a few physicists with far out ideas, but they usually came up with those ideas after a long and successful career studying something else.
I've seen squid ink for sale in specialty stores and ethnic markets. I associate it with making black rice, but there are pastas and sauces that use it in various places around the world already.
Looks more like Tivo is edging into the lower end of commercial recorders, which can easily have a dozen or more tuners in some rack mount setup. Those get used for anything from weird security video setups to shows that need to record all 24 hr news stations or other content on TV
Reminds me of the hunting and fishing pictures that border on bad perspective tricks, putting the catch way in front of something to make it look bigger... with 6-10 inch long gulf shrimp were not too uncommon from what I remember. Not to say the one they caught is not as big as they say it is, just the pictures could have done a much better job of conveying the size.
From what I remember, the Ocean Ranger wasn't involved in a situation with a rogue wave, but in a chain of unfortunate competence/training failures, including the water coming in a port hole that should have had a protective plate installed, but did not at the time. Looking it up, the place of ingress of water was only about 8m above sea level, and the Grand Banks gets seas of that size quite regularly, with 15+ m seas not unheard of (e.g. at the time of the incident...). Otherwise it was rated for waves much larger than that which could even handle a wave freakishly over the significant wave height in storms.
These days there are a lot of statistics on typical wave height for different coastlines and chances of even rogue waves, and it is something that can be evaluated. 20 m is pretty high, and shallow, coastal areas tend to have a deficit of extremely high waves compared to open ocean. But it could come down to the particular location, as there are plenty that have never seen anything close to waves big enough to hit that even in strong hurricanes.
The question isn't asking what the chances of a particular child is boy or female, which would be 50%, but what are the chances a family with two children, would be both boys, or have one boy, knowing it isn't two girls.
This is not just something that is a matter of trivia, but has real world impact. For example, this is how the probabilities work for any textbook simple genotype case. Suppose you had a recessive and dominant gene, such that there is no impact of being a mixed genotype, but a double recessive dies before birth. Order obviously doesn't matter here, only that you either have two different genes, or you have two of the same genes of one or the other. For two parents of mixed genotype, offspring get the genes randomly, so it is just like coin flips, and you will get 25% DD, 50% Dr, and 25% rr. All of the rr will die before birth, resulting in a third of the offspring being DD, and two-thirds being Dr.
You can just look at the number of families that have kids, and see that half of them will have a mix, while a quarter have two girls, and a quarter will have two boys. Or just start doing this with coins. I even sat down with an online coin flipper, and did 100 quick flips, getting 22 MM (or HH), 54 MF (HT) and 24 FF (TT). Excluding the FF case leaves behind two groups without a 50-50 ratio, even if there are only two possibilities.
And if I remember correctly that you were the one with a biology background, think of genotypes (which I mention in another comment below).
No, the answer is one third, and you can check it by doing an experiment with coins (or an Excel spread sheet, or simple program). The key point is they are not giving info about one child and asking for the chance of a specific child being male or female, but saying "one" and "the other" places constraints only on the whole system. If you flip two coins, there are four equal possibilities: TT, TH, HT, HH. Even if not keeping track of order, it is TT, HT, HH with a 25%:50%:25% split. The information given allows you to only eliminate one of those (say TT), and not say which coin is heads, and either way end up with a 1:3 ratio.
You can literally test this with coins. Flip a pair of coins. If the pair is TT, don't count it and reflip. Otherwise record how many times you get HH and how many times you get one of each. With about 25 flips, you should have less than a 5% chance of getting 50% or higher. 100 flips would give you less than a thousand chance of getting 50% or more HH, and about 5% chance of getting more than 40% HH, at which point it would be rather tedious but separated from 50%.
This question comes up a lot in three contexts: lessons about the subtle meanings of words in word problems, basic level combinators/probability, or random "paradox" lists. But even like the Monty Hall probability question, people will argue until against the results of even basic experiments until the day they die.
From what I've seen before, it basically had four radiation detectors: Geiger-Muller tube counter (which unfortunately is and was kind of expensive, leading to cheaper kits with everything else), an electroscope, which is something you can build from household items, a phosphor based detector, and a cloud chamber. A cloud chamber lets you see paths of ionizing radiation and building one was one of the more fond memories I had from middle school. The kit also had a selection of small radioactive sources , something else still available from educational supplies (price has gone up a lot in the couple decades since I last bought some). These are not particularly dangerous as long as they are kept outside of the body, like a lot of things in our day-to-day life.
And for that matter, elemental and many other forms of mercury have virtually no evidence linking it to causing cancer in humans, with some evidence in animals for methymercury. It is still a very dangerous substance without care and not something I would give to a kid, but it is not dangerous because it causes cancer.
1 (h) the weapon sometimes known as a “shuriken”, “shaken” or “death star”, being a hard non-flexible plate having three or more sharp radiating points and designed to be thrown;
These days there are a lot of statistics on typical wave height for different coastlines and chances of even rogue waves, and it is something that can be evaluated. 20 m is pretty high, and shallow, coastal areas tend to have a deficit of extremely high waves compared to open ocean. But it could come down to the particular location, as there are plenty that have never seen anything close to waves big enough to hit that even in strong hurricanes.